Far Eastern Mathematical Journal

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On two broad classes of heavy-tailed distributions


Chun Su, Zhishui Hu

2004, issue 2, Ñ. 195–204


Abstract
Since the introduction of Class $\mathcal{M}$ and Class $\mathcal{M^?}$, they have played important roles in insurance to describe tail equivalence of ruin probability and tail behavior of the deficit at ruin. And in insurance and finance most of heavy-tailed distributions with finite and positive expectations belong to Class $\mathcal{M}$. So it is important to study tail behaviors of Class $\mathcal{M}$ and Class $\mathcal{M^?}$. In this paper, we obtain some results on essential tail behaviors of these two classes.

Keywords:
class $\mathcal{M}$, class $\mathcal{M^?}$, class $\mathcal{D}$, tail behaviors

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References

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